{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PCA for Algorithmic Trading: Eigen Portfolios"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports & Settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T14:19:50.331659Z",
     "start_time": "2020-06-18T14:19:50.329374Z"
    }
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T14:19:50.862864Z",
     "start_time": "2020-06-18T14:19:50.333663Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.preprocessing import scale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T14:19:50.866571Z",
     "start_time": "2020-06-18T14:19:50.864177Z"
    }
   },
   "outputs": [],
   "source": [
    "sns.set_style('white')\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Eigenportfolios"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another application of PCA involves the covariance matrix of the normalized returns. The principal components of the correlation matrix capture most of the covariation among assets in descending order and are mutually uncorrelated. Moreover, we can use standardized the principal components as portfolio weights.\n",
    "\n",
    "Let’s use the 30 largest stocks with data for the 2010-2018 period to facilitate the exposition:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data Preparation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T14:19:52.921865Z",
     "start_time": "2020-06-18T14:19:50.867865Z"
    }
   },
   "outputs": [],
   "source": [
    "idx = pd.IndexSlice\n",
    "with pd.HDFStore('../../data/assets.h5') as store:\n",
    "    stocks = store['us_equities/stocks'].marketcap.nlargest(30)\n",
    "    returns = (store['quandl/wiki/prices']\n",
    "               .loc[idx['2010': '2018', stocks.index], 'adj_close']\n",
    "               .unstack('ticker')\n",
    "               .pct_change())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We again winsorize and also normalize the returns:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T14:19:52.972829Z",
     "start_time": "2020-06-18T14:19:52.922836Z"
    }
   },
   "outputs": [],
   "source": [
    "normed_returns = scale(returns\n",
    "                       .clip(lower=returns.quantile(q=.025), \n",
    "                             upper=returns.quantile(q=.975), \n",
    "                             axis=1)\n",
    "                      .apply(lambda x: x.sub(x.mean()).div(x.std())))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T14:19:52.985094Z",
     "start_time": "2020-06-18T14:19:52.973751Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "DatetimeIndex: 2070 entries, 2010-01-05 to 2018-03-27\n",
      "Data columns (total 23 columns):\n",
      " #   Column  Non-Null Count  Dtype  \n",
      "---  ------  --------------  -----  \n",
      " 0   AAPL    2070 non-null   float64\n",
      " 1   AMZN    2070 non-null   float64\n",
      " 2   BA      2070 non-null   float64\n",
      " 3   BAC     2070 non-null   float64\n",
      " 4   CSCO    2070 non-null   float64\n",
      " 5   CVX     2070 non-null   float64\n",
      " 6   GOOGL   2070 non-null   float64\n",
      " 7   HD      2070 non-null   float64\n",
      " 8   INTC    2070 non-null   float64\n",
      " 9   JNJ     2070 non-null   float64\n",
      " 10  JPM     2070 non-null   float64\n",
      " 11  KO      2070 non-null   float64\n",
      " 12  MA      2070 non-null   float64\n",
      " 13  MSFT    2070 non-null   float64\n",
      " 14  PFE     2070 non-null   float64\n",
      " 15  PG      2070 non-null   float64\n",
      " 16  T       2070 non-null   float64\n",
      " 17  UNH     2070 non-null   float64\n",
      " 18  V       2070 non-null   float64\n",
      " 19  VZ      2070 non-null   float64\n",
      " 20  WFC     2070 non-null   float64\n",
      " 21  WMT     2070 non-null   float64\n",
      " 22  XOM     2070 non-null   float64\n",
      "dtypes: float64(23)\n",
      "memory usage: 388.1 KB\n"
     ]
    }
   ],
   "source": [
    "returns = returns.dropna(thresh=int(returns.shape[0] * .95), axis=1)\n",
    "returns = returns.dropna(thresh=int(returns.shape[1] * .95))\n",
    "returns.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T14:19:53.022417Z",
     "start_time": "2020-06-18T14:19:52.986778Z"
    }
   },
   "outputs": [],
   "source": [
    "cov = returns.cov()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T14:19:53.533028Z",
     "start_time": "2020-06-18T14:19:53.023680Z"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.clustermap(cov);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Run PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After dropping assets and trading days as in the previous example, we are left with 23 assets and over 2,000 trading days. We estimate all principal components and find that the two largest explain 57.6% and 12.4% of the covariation, respectively:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T14:19:53.577975Z",
     "start_time": "2020-06-18T14:19:53.533908Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style  type=\"text/css\" >\n",
       "</style><table id=\"T_c7420382_b16e_11ea_b35f_6045cb72e6b3\" ><thead>    <tr>        <th class=\"blank level0\" ></th>        <th class=\"col_heading level0 col0\" >Explained Variance</th>    </tr></thead><tbody>\n",
       "                <tr>\n",
       "                        <th id=\"T_c7420382_b16e_11ea_b35f_6045cb72e6b3level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "                        <td id=\"T_c7420382_b16e_11ea_b35f_6045cb72e6b3row0_col0\" class=\"data row0 col0\" >55.90%</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_c7420382_b16e_11ea_b35f_6045cb72e6b3level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "                        <td id=\"T_c7420382_b16e_11ea_b35f_6045cb72e6b3row1_col0\" class=\"data row1 col0\" >15.52%</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_c7420382_b16e_11ea_b35f_6045cb72e6b3level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "                        <td id=\"T_c7420382_b16e_11ea_b35f_6045cb72e6b3row2_col0\" class=\"data row2 col0\" >5.36%</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_c7420382_b16e_11ea_b35f_6045cb72e6b3level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "                        <td id=\"T_c7420382_b16e_11ea_b35f_6045cb72e6b3row3_col0\" class=\"data row3 col0\" >4.85%</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_c7420382_b16e_11ea_b35f_6045cb72e6b3level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "                        <td id=\"T_c7420382_b16e_11ea_b35f_6045cb72e6b3row4_col0\" class=\"data row4 col0\" >3.32%</td>\n",
       "            </tr>\n",
       "    </tbody></table>"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x7f2cbe453590>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA()\n",
    "pca.fit(cov)\n",
    "pd.Series(pca.explained_variance_ratio_).to_frame('Explained Variance').head().style.format('{:,.2%}'.format)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create PF weights from principal components"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we select and normalize the four largest components so that they sum to 1 and we can use them as weights for portfolios that we can compare to an equal-weighted portfolio formed from all stocks::"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T14:19:53.583593Z",
     "start_time": "2020-06-18T14:19:53.579240Z"
    }
   },
   "outputs": [],
   "source": [
    "top4 = pd.DataFrame(pca.components_[:4], columns=cov.columns)\n",
    "eigen_portfolios = top4.div(top4.sum(1), axis=0)\n",
    "eigen_portfolios.index = [f'Portfolio {i}' for i in range(1, 5)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Eigenportfolio Weights"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The weights show distinct emphasis, e.g., portfolio 3 puts large weights on Mastercard and Visa, the two payment processors in the sampel whereas potfolio 2 has more exposure to some technology companies:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T14:19:54.462300Z",
     "start_time": "2020-06-18T14:19:53.584932Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x576 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "axes = eigen_portfolios.T.plot.bar(subplots=True,\n",
    "                                   layout=(2, 2),\n",
    "                                   figsize=(14, 8),\n",
    "                                   legend=False)\n",
    "for ax in axes.flatten():\n",
    "    ax.set_ylabel('Portfolio Weight')\n",
    "    ax.set_xlabel('')\n",
    "sns.despine()\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Eigenportfolio Performance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When comparing the performance of each portfolio over the sample period to ‘the market’ consisting of our small sample, we find that portfolio 1 performs very similarly, whereas the other portfolios capture different return patterns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T14:19:55.291424Z",
     "start_time": "2020-06-18T14:19:54.463212Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(14, 6), sharex=True)\n",
    "axes = axes.flatten()\n",
    "returns.mean(1).add(1).cumprod().sub(1).plot(title='The Market', ax=axes[0])\n",
    "for i in range(3):\n",
    "    rc = returns.mul(eigen_portfolios.iloc[i]).sum(1).add(1).cumprod().sub(1)\n",
    "    rc.plot(title=f'Portfolio {i+1}', ax=axes[i+1], lw=1, rot=0)\n",
    "\n",
    "for i in range(4):\n",
    "    axes[i].set_xlabel('')\n",
    "sns.despine()\n",
    "fig.tight_layout()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": true,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
